Fedunov R.G., Yermolenko I.P. Accelerated Calculation of Integrals in the Theory of Non-Thermal Electron Transfer

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https://doi.org/10.15688/mpcm.jvolsu.2018.3.5

Roman Gennadyevich Fedunov
Candidate of Physical and Mathematical Sciences, Associate Professor,
Department of Theoretical Physics and Wave Processes,
Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Igor Petrovich Yermolenko
Master Student, Department of Theoretical Physics and Wave Processes,
Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. In this article we’ve carried out a modification of the expression for calculating the probability of non-thermal electron transfer in a two-level system obtained in the framework of the nonstationary second-order perturbation theory for electron interaction. This expression takes into account the reorganization of the environment (Debye model) and high-frequency intramolecular vibrational modes (quantum mechanical description). Since the “Debye” part is characterized by slow relaxation times, which significantly exceed the period of intramolecular vibrations, the “quantum” part will be a rapidly oscillating function included in the integral. As a result, computing two-dimensional integral using simple grid methods may require significant computational resources. To speed up the calculation of this integral, we propose a Gauss quadrature formula. It is shown that, in the high-temperature limit, the quadrature formula can be successfully applied in the theory of non-thermal electron transfer and increases the calculation speed of the integral by two orders of magnitude.

Key words: electron transfer, nonstationary perturbation theory, quadrature formula, intramolecular high-frequency modes.

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Accelerated Calculation of Integrals in the Theory of Non-Thermal  Electron Transfer by Fedunov R.G., Yermolenko I.P. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. Vol. 21 No. 3 2018, pp. 48-57

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